Exact local phase readout in commuting spin stars and noise selection of balanced three-qubit decoding

This theoretical and computational preprint studies how the direction of central-qubit noise affects optimal local readout of a multipartite GHZ phase. The task is equal-prior discrimination of GHZ+ and GHZ- by a final measurement of one central qubit, using commuting spin-star interactions with fixed axes and a bound on the instantaneous sum of absolute coupling strengths. For signed, time-dependent controls, the study derives an exact attainable trace-distance frontier and its inverse error-time relation. Equal integrated coupling angles attain the noiseless frontier, so balanced simultaneous and sequential schedules are equivalent under the stated resource model. Central dephasing along the commuting axis preserves this equivalence and gives an exact optimal stopping time. The main additional result concerns three qubits with transverse central Pauli-jump noise. Among nonnegative deterministic controls that achieve perfect noiseless discrimination at the minimum possible decoding time, balanced simultaneous couplings are uniquely optimal at every finite positive noise rate. The proof establishes nonnegativity of the signed contrast, an exact performance-gap identity, and a lower bound in terms of accumulated coupling imbalance. Optimality is restricted to this control class and endpoint time; allowing a later measurement can improve the result. The supplementary materials contain supporting proofs, calibration bounds and classical scalar-output prediction results. The companion RM01 analysis compares finite-sample prediction and serialized storage against methods using the same measurement information. It explicitly identifies cases where a conventional polynomial representation uses fewer bytes, and does not claim a new general compression principle. The archive supplies editable manuscript sources, code, simulated data, recorded results, reproduction instructions and checksums. Archived validation includes 2,348 Q1 assertions and 530 transverse-noise schedule cases. A publication review dated 4 November 2026 adds separate numerical checks and a fresh reproduction of the RM01 analysis of 12,000 simulated measurement records. Its report distinguishes newly executed checks from archived results and documents execution limitations. All findings concern the specified mathematical and simulation models. No laboratory measurements or device-level advantage are reported. AI assistance is disclosed. Scientific priority and independent human peer review are not established.